Heterojunction solar cells based on colloidal nanocrystals (NCs) have shown remarkable improvements in performance in the last decade, but this progress is limited to merely two materials, PbS and PbSe. However, solar cells based on other material systems such as copper-based compounds show lower power conversion efficiencies and much less effort has been made to develop a better understanding of factors limiting their performance. Here, we study charge carrier loss mechanisms in solution-processed CuInS2/ZnO NC solar cells by combining steady-state measurements with transient photocurrent and photovoltage measurements. We demonstrate the presence of an extraction barrier at the CuInS2/ZnO interface, which can be reduced upon illumination with UV light. However, trap-assisted recombination in the CuInS2 layer is shown to be the dominant decay process in these devices.